Calculating Past City Population with Annual Growth

Problem Analysis

We are given the current population of a city and the annual growth rate. We need to find the population from 2 years ago.

• Current Population ($P_{current}$) = 11,02,500
• Annual Growth Rate ($R$) = 5%
• Time Period ($T$) = 2 years
• We need to find the Past Population ($P_{past}$).

Population Calculation Formula

The formula relating current population to past population with a constant annual growth rate is:

$P_{current} = P_{past} \times (1 + \frac{R}{100})^T$

To find the past population, we rearrange the formula:

$P_{past} = \frac{P_{current}}{(1 + \frac{R}{100})^T}$

Step-by-Step Solution

1. Substitute the values into the formula:
   $P_{past} = \frac{11,02,500}{(1 + \frac{5}{100})^2}$
2. Calculate the term inside the parenthesis:
   $1 + \frac{5}{100} = 1 + 0.05 = 1.05$
3. Calculate the denominator (growth factor raised to the power of time):
   $(1.05)^2 = 1.1025$
4. Divide the current population by the calculated factor:
   $P_{past} = \frac{11,02,500}{1.1025}$
5. Final Calculation:
   $P_{past} = 10,00,000$

Conclusion

The population of the city 2 years ago was 10,00,000.